Abstract In this paper we consider the problem of position tracking and error boundedness for a master–slave teleoperation system when the communication channel is characterized by a time-varying stochastic delay. In particular, we assume the delay to be a time-varying Markov regime switching process. Our solution is based on a suitable proportional–derivative (PD) like controller. Exploiting a Lyapunov–Krasovskii functional approach, we are able to show that the velocity and position errors remain bounded, provided specific inequality is satisfied. Moreover, zero steady-state position error is achieved when the human operator and the environment do not interact with the system. In order to be able to exploit Lyapunov–Krasovskii approach we need to lift the underlying process to an infinite-dimensional process taking values in a suitable Banach space so that, in the new space, the process is a Markov process. Our conditions for guaranteeing boundedness and the zero steady-state position tracking error are the natural generalization of the deterministic counterparts available in the literature, i.e. when considering the trivial case of a single-state Markov process previous results are recovered. Simulation results show the effectiveness of the proposed approach.

中文翻译：

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具有非对称随机延迟的双边远程操作员的稳定性

摘要 在本文中，我们考虑了当通信信道具有时变随机延迟特征时主从遥操作系统的位置跟踪和误差有界问题。特别地，我们假设延迟是一个随时间变化的马尔可夫状态转换过程。我们的解决方案基于合适的比例微分 (PD) 之类的控制器。利用 Lyapunov-Krasovskii 函数方法，我们能够证明速度和位置误差保持有界，前提是满足特定的不等式。此外，当操作人员和环境不与系统交互时，可实现零稳态位置误差。为了能够利用 Lyapunov-Krasovskii 方法，我们需要将底层过程提升为在合适的 Banach 空间中取值的无限维过程，以便在新空间中，该过程是马尔可夫过程。我们保证有界性和零稳态位置跟踪误差的条件是文献中可用的确定性对应物的自然概括，即当考虑单态马尔可夫过程的平凡情况时，恢复先前的结果。仿真结果表明了所提出方法的有效性。当考虑单状态马尔可夫过程的微不足道的情况时，可以恢复先前的结果。仿真结果表明了所提出方法的有效性。当考虑单状态马尔可夫过程的微不足道的情况时，可以恢复先前的结果。仿真结果表明了所提出方法的有效性。